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                数列的GCD                </h1>
                <p>时间限制：10s&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  空间限制：256MB</p>			</div>
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                                <h3>题目描述</h3><p><div>给出一个长度为N的数列{a[n]}，1&lt;=a[i]&lt;=M(1&lt;=i&lt;=N)。&nbsp;</div>
<div>现在问题是，对于1到M的每个整数d，有多少个不同的数列b[1], b[2], ..., b[N]，满足：&nbsp;</div>
<div>(1)1&lt;=b[i]&lt;=M(1&lt;=i&lt;=N)；&nbsp;</div>
<div>(2)gcd(b[1], b[2], ..., b[N])=d；&nbsp;</div>
<div>(3)恰好有K个位置i使得a[i]&lt;&gt;b[i](1&lt;=i&lt;=N)&nbsp;</div>
<div>注：gcd(x1,x2,...,xn)为x1, x2, ..., xn的最大公约数。&nbsp;</div>
<div>输出答案对1,000,000,007取模的值。&nbsp;</div>
<div></div>
<p></p></p><hr/><h3>输入格式</h3><p><div>第一行包含3个整数，N，M，K。&nbsp;</div>
<div>第二行包含N个整数：a[1], a[2], ..., a[N]。&nbsp;</div>
<div></div>
<p></p></p><hr/><h3>输出格式</h3><p><div>输出M个整数到一行，第i个整数为当d=i时满足条件的不同数列{b[n]}的数目mod 1,000,000,007的值。&nbsp;</div>
<div></div>
<p></p></p><hr/><h3>样例输入</h3><pre>3 3 3
3 3 3</pre><hr/><h3>样例输出</h3><pre>7 1 0</pre><hr/><h3>提示</h3><p><div>当d=1，{b[n]}可以为：(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1), (2, 1, 2), (2, 2, 1)。&nbsp;</div>
<div>当d=2，{b[n]}可以为：(2, 2, 2)。&nbsp;</div>
<div>当d=3，因为{b[n]}必须要有k个数与{a[n]}不同，所以{b[n]}不能为(3, 3, 3)，满足条件的一个都没有。&nbsp;</div>
<div>对于100%的数据，1&lt;=N,M&lt;=300000, 1&lt;=K&lt;=N, 1&lt;=a[i]&lt;=M。&nbsp;</div>
<p></p></p><hr/><h3>题目来源</h3><p>没有写明来源</p>
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